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Modulus of a Complex Number

I. If x-y=x...

Question

I. If $x - y = x y = 1 - x - y$ , then $x + y$ is $\frac{5}{6}$
II. The system of equations $3 x + 2 y = a$ and $5 x + b y = 4$ has infinitely many solutions for x and y, then $a = 4, b = 3$
Which is true?

A

I only

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B

II only

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C

Both I and II

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D

None of these

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Solution

The correct option is A I only
$S t a t e m e n t A - G i v e n x - y = x y - - - (1) 1 - x - y = x y - - - (2) a n d x - y = 1 - x - y - - - (3) \Rightarrow x - y + x + y = 1 \Rightarrow 2 x = 1 \Rightarrow x = \frac{1}{2} - - - (4) S u b s t i t u t i n g x = \frac{1}{2} i n (1) w e g e t \frac{1}{2} - y = \frac{1}{2} y \Rightarrow y = \frac{1}{3} - - - (5) A d d i n g (4) a n d (5) w e g e t x + y = \frac{1}{2} + \frac{1}{3} = \frac{5}{6} S o, t h i s s t a t e m e n t i s t r u e . S t a t e m e n t B - W e h a v e 3 x + 2 y = a a n d 5 x + b y = 4. P u t t i n g a = 4 a n d b = 3 w e g e t 5 x + 3 y = 4 a n d 3 x + 2 y = 4 W e s e e t h a t c o e f f i c i e n t o f x a n d y i n t h e e q u a t i o n s a r e d i f f e r e n t . S o, t h e s y s t e m i s c o n s i s t e n t a n d t h e y d o n o t h a v e i n f i n i t e s o l u t i o n . S o, s t a t e m e n t B i s n o t t r u e . S t a t e m e n t D - I t i s o b v i o u s l y i n c o r r e c t a s s t a t e m e n t A i s c o r r e c t .$

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Similar questions

x - y = x y = 1 - x - y,

x + y

\frac{5}{6}

II. The system of equations

3 x + 2 y = a

5 x + b y = 4

has infinitely many solutions for

x

y

a = 4

b = 3

\frac{x}{a} + \frac{y}{b} = 2

a x - b y = a^{2} - b^{2}

x = a, y = b

Q. (i) Prove that there is a value of c(≠ 0) for which the system
6x + 3y = c − 3
12x + cy = c has infinitely many solutions. Find this value.

(ii) Find c if the system of equations cx + 3y + 3 – c = 0, 12x + cy – c = 0 has infinitely many solutions?

Q. If the system of linear equations

2 x + p y + 6 z = 8

x + 2 y + q z = 5

x + y + 3 z = 4

has infinitely many solutions, then a possible pair of

p

q

Q. The system of equations

2 x + p y + 6 z = 8

x + 2 y + q z = 5

x + y + 3 z = 4

has infinitely many solutions, then

p = ?

Q. If the system of equations 2x + 3y = 5, 4x + ky = 10 has infinitely many solutions, then k =

(a) 1
(b) ½
(c) 3
(d) 6

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